Proposition 2.1 [1]}
Let \(\mathcal {C}\)  be the annulus \(\lbrace \xi \in \mathbb {R}^d:\frac{3}{4}\le |\xi |\le \frac{8}{3}\rbrace \) . There exist radial function \(\varphi \) , valued in the interval \([0,1]\) , belonging respectively to \(\mathcal {D}(\mathcal {C})\) , and such that
\( \forall \xi \in \mathbb {R}^d\backslash \lbrace 0\rbrace ,\ \sum _{j\in \mathbb {Z}}\varphi (2^{-j}\xi )=1, \) 
\( |j-j^{\prime }|\ge 2\Rightarrow \mathrm {Supp}\ \varphi (2^{-j}\cdot )\cap \mathrm {Supp}\ \varphi (2^{-j^{\prime }}\cdot )=\emptyset . \) 
